1. The problem asks for the contrapositive of the implication $ (p \lor q) \to r $. 2. Recall the contrapositive of an implication $ A \to B $ is $ \neg B \to \neg A $. 3. Here, $ A = p \lor q $ and $ B = r $. 4. Applying the contrapositive formula: $$ \neg r \to \neg (p \lor q) $$ 5. Using De Morgan's law, $ \neg (p \lor q) = \neg p \land \neg q $. 6. So the contrapositive is: $$ \neg r \to (\neg p \land \neg q) $$ 7. Now, let's compare with the options: - Option 1: $ (\neg p \land \neg q) \to r $ (This is the converse of the contrapositive, not correct) - Option 2: $ \neg r \to (\neg p \lor \neg q) $ (Incorrect because of $\lor$ instead of $\land$) - Option 3: $ \neg r \to \neg (p \lor q) $ (This matches step 4, the contrapositive before applying De Morgan's law) - Option 4: $ r \to (p \lor q) $ (This is the converse of the original implication, not correct) 8. Therefore, the contrapositive is exactly option 3: $ \neg r \to \neg (p \lor q) $. Final answer: Option 3